err.log shows:
Error: The module '/var/www/onlyoffice/documentserver/server/SpellChecker/node_modules/nodehun/build/Release/nodehun.node'
was compiled against a different Node.js version using
NODE_MODULE_VERSION 57. This version of Node.js requires
NODE_MODULE_VERSION 67. Please try re-compiling or re-installing
the module (for instance, using `npm rebuild` or `npm install`).
at Object.Module._extensions..node (internal/modules/cjs/loader.js:751:18)
at Module.load (internal/modules/cjs/loader.js:620:32)
at tryModuleLoad (internal/modules/cjs/loader.js:560:12)
at Function.Module._load (internal/modules/cjs/loader.js:552:3)
at Module.require (internal/modules/cjs/loader.js:658:17)
at require (internal/modules/cjs/helpers.js:22:18)
at Object.<anonymous> (/var/www/onlyoffice/documentserver/server/SpellChecker/sources/spellCheck.js:13:17)
at Module._compile (internal/modules/cjs/loader.js:722:30)
at Object.Module._extensions..js (internal/modules/cjs/loader.js:733:10)
at Module.load (internal/modules/cjs/loader.js:620:32)
internal/modules/cjs/loader.js:751
return process.dlopen(module, path.toNamespacedPath(filename));
^

When running the node command for the server.js command manually I get the following output:

root@Lenz:/etc/onlyoffice/documentserver# node /var/www/onlyoffice/documentserver/server/SpellChecker/sources/server.js
WARNING: No configurations found in configuration directory:/etc/onlyoffice/documentserver/config
WARNING: To disable this warning set SUPPRESS_NO_CONFIG_WARNING in the environment.
/var/www/onlyoffice/documentserver/server/SpellChecker/node_modules/config/lib/config.js:203
throw new Error('Configuration property "' + property + '" is not defined');
^

Error: Configuration property "SpellChecker" is not defined
at Config.get (/var/www/onlyoffice/documentserver/server/SpellChecker/node_modules/config/lib/config.js:203:11)
at Object.<anonymous> (/var/www/onlyoffice/documentserver/server/SpellChecker/sources/server.js:12:34)
at Module._compile (internal/modules/cjs/loader.js:722:30)
at Object.Module._extensions..js (internal/modules/cjs/loader.js:733:10)
at Module.load (internal/modules/cjs/loader.js:620:32)
at tryModuleLoad (internal/modules/cjs/loader.js:560:12)
at Function.Module._load (internal/modules/cjs/loader.js:552:3)
at Function.Module.runMain (internal/modules/cjs/loader.js:775:12)
at startup (internal/bootstrap/node.js:300:19)
at bootstrapNodeJSCore (internal/bootstrap/node.js:826:3)

When checking the /etc/onlyoffice/documentserver/default.json file it is as the original on github.

This is the reason of the issue. NodeJS version required for Document Server's functioning is 8.x. Please install it and check if the issue persists. If there is no possibility to downgrade NodeJS, please use the docker installation of DS instead.